In the 1980s, physicists working on String Theory discovered a phenomena called Mirror Symmetry: the idea is that tha same physical theory can be described by two mathematically different models. Naively, one of this models (the A-model) is mainly related to the symplectic geometry of Calabi-Yau manifolds, while the other one (B-model) is related to the complex algebraic geometry of these spaces. Although many of the tools used by these physicists were not yet rigorous, this led to some impressing purely mathematical results. The most famous example is the quintic threefold: mirror symmetry associates, to a generic quintic threefold in \(P^4\) , a family of manifolds known as mirror quintics. In the paper [1]}, published in 1991, the authors used these techniques to make predictions for the number of rational curves on a generic quintic threefold in \(P^4\) . What they did was to assume that the correlation functions from the A-model and the B-model were the same.The first was associated to Gromov-Witten invariants and a prediction to the number of rational curves on a general quintic, and the second were computed explicitly. This correlation function is usually called Yukawa coupling.
